"Too drunk to fucktion" is a more specified spin-off from the term "too drunk to function" referring to someone being so intoxicated from alcohol that they can no longer perform even the simplest sexual acts with someone. This includes but is not limited to kissing, de-clothing either oneself or another, fellatio, cunnilingus, vaginal and anal intercourse. Once someone has reached this level of intoxication, it is often followed by violent vomiting and/or passing the fuck out.

Nick: "Hey, you're really drunk. You could barely get your shirt off in that game of strip poker. "
Evan: "Yeah and when I was trying to make out with you earlier you kept licking my face instead"
Kitty: "That's..cause...I'm....too drunk to fucktion!" (Kitty begins puking into a beer pong cup)